Titlebook: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations; Xinyuan Wu,Bin Wang Book 2018 Springer Natu

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An Energy-Preserving and Symmetric Scheme for Nonlinear Hamiltonian Wave Equations,the energy of the underlying Hamiltonian wave equations. To this end, we first define and discuss the bounded operator-argument functions on the underlying domain. We then introduce an operator-variation-of-constants formula, based on which we present an energy-preserving scheme for nonlinear Hamilt

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,Arbitrarily High-Order Time-Stepping Schemes for Nonlinear Klein–Gordon Equations,ry conditions. We first formulate an abstract ordinary differential equation (ODE) on a suitable infinite–dimensional function space based on the operator spectrum theory. We then introduce an operator-variation-of-constants formula for the nonlinear abstract ODE. The nonlinear stability and converg

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An Essential Extension of the Finite-Energy Condition for ERKN Integrators Solving Nonlinear Wave Eonlinear wave equations. We begin with an error analysis of ERKN integrators for multi-frequency highly oscillatory systems ., where . is positive semi-definite, .. These highly oscillatory problems arise from the semi-discretisation of conservative or dissipative nonlinear wave equations. The struc

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Exponential Fourier Collocation Methods for First-Order Differential Equations,. We discuss in detail the connections of EFCMs with trigonometric Fourier collocation methods (TFCMs), the well-known Hamiltonian Boundary Value Methods (HBVMs), Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an extension, in a strict mathematical sense, of these existing methods in the literature.

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